I know that there are no gods.

[Edwardo Piet]

The problem lies in your definition of 'knowledge as being not merely awareness but self-awareness, DvF.

I don't define knowledge as self-awareness I define it as awareness. Self-awareness is self-knowledge.

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But in DvF's description once you have examined the table as thoroughly as possible you are aware of it in every sense.

No, not at all. You are aware that it exists but you don't know if it exists as an imaginary table or a real table.

You may be aware that China exists, but to act upon that is to act upon the knowledge that China exists by, say, going to China. It requires both the assumption that China exists and that the awareness one has of China is not faulty.

If I am aware that China exists then I know that China exists.

China may be an illusion but then I'm still aware of the illusion of China.

The question is, is the China that I am aware of/that I know of, real?

I don't know/I am not aware. Knowing of something and knowing what it is or if it is real is another matter.

Knowing that something is is being aware of its existence whether that's a real or illusory existence. Knowing what something is is being aware of its essence.

I'll now concede something: My argument for knowing that there are no gods only works on omnipresent gods.

My argument goes like this: Omnipresent gods are present in all things.

The things that I am aware of therefore, must have omnipresent gods present in them, if any omnipresent gods exist.

Since omnipresent gods probably don't exist, the things that I am aware of are probably without their presence.

So, I claim "I know that/I am aware there are no[omnipresent] gods" as a statement of opinion which is probably true. I probably am aware of the absence of omnipresent gods rather than any of their omnipresence.